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Simplifying 14x2 + 11x + -20 = 0 Reorder the terms: -20 + 11x + 14x2 = 0 Solving -20 + 11x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.428571429 + 0.7857142857x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 0.7857142857x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 0.7857142857x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 0.7857142857x + x2 = 0 + 1.428571429 0.7857142857x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 0.7857142857x + x2 = 1.428571429 The x term is 0.7857142857x. Take half its coefficient (0.3928571429). Square it (0.1543367347) and add it to both sides. Add '0.1543367347' to each side of the equation. 0.7857142857x + 0.1543367347 + x2 = 1.428571429 + 0.1543367347 Reorder the terms: 0.1543367347 + 0.7857142857x + x2 = 1.428571429 + 0.1543367347 Combine like terms: 1.428571429 + 0.1543367347 = 1.5829081637 0.1543367347 + 0.7857142857x + x2 = 1.5829081637 Factor a perfect square on the left side: (x + 0.3928571429)(x + 0.3928571429) = 1.5829081637 Calculate the square root of the right side: 1.258136783 Break this problem into two subproblems by setting (x + 0.3928571429) equal to 1.258136783 and -1.258136783.Subproblem 1
x + 0.3928571429 = 1.258136783 Simplifying x + 0.3928571429 = 1.258136783 Reorder the terms: 0.3928571429 + x = 1.258136783 Solving 0.3928571429 + x = 1.258136783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3928571429' to each side of the equation. 0.3928571429 + -0.3928571429 + x = 1.258136783 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + x = 1.258136783 + -0.3928571429 x = 1.258136783 + -0.3928571429 Combine like terms: 1.258136783 + -0.3928571429 = 0.8652796401 x = 0.8652796401 Simplifying x = 0.8652796401Subproblem 2
x + 0.3928571429 = -1.258136783 Simplifying x + 0.3928571429 = -1.258136783 Reorder the terms: 0.3928571429 + x = -1.258136783 Solving 0.3928571429 + x = -1.258136783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3928571429' to each side of the equation. 0.3928571429 + -0.3928571429 + x = -1.258136783 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + x = -1.258136783 + -0.3928571429 x = -1.258136783 + -0.3928571429 Combine like terms: -1.258136783 + -0.3928571429 = -1.6509939259 x = -1.6509939259 Simplifying x = -1.6509939259Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8652796401, -1.6509939259}
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